Question

An electron is revolving round the nucleus (stationary) of charge 'Ze'. The amount of energy '47.2 eV' is required to transit the electron from 2nd orbit to 3rd orbit.What is the value of 'Z' ?

Answer 1

We know from Bohr's model that energy of a single electron in state `n` in Hydrogen like atom having atomic number `Z` is given by

`E_n=E_1Z^2/n^2`
where `E_1=-13.6\ eV`

For the given transition

`DeltaE=47.2=-13.6Z^2(1/3^2-1/2^2)`
`=>47.2=13.6Z^2xx5/36`
`=>Z=sqrt(47.2/13.6xx36/5)`
`=>Z=5`